If you see a pattern in the surrounding around you, can you draw a conclusion? Let’s say it rains on 2nd, 4th, 6th, 8th and so on… date of the July month, observing the pattern, can we induce if will it rain on 16th? Well, this can be done with the help of the principle of Mathematical Induction. Let’s find out more in the section below.
FAQ on Principle of Mathematical Induction
Question 1: Who invented mathematical induction?
Answer: Giovanni Vacca invented mathematical induction. He was an Italian mathematician (1872-1953) and was also assistant to Giuseppe Peano and historian of science in his: G. Vacca, Maurolycus, the first discoverer of the principle of mathematical induction (1909).
Question 2: What is a strong mathematical induction?
Answer: Strong mathematical induction is a kind of proof that closely relates to simply induction. In other words, in simple induction, we have a statement P (n) about the whole number n, thus we want to prove that P (n) is true for every value of n.
Question 3: Why is mathematical induction important?
Answer: Mathematical induction is essential because it helps in characterizing the natural numbers. Thus, this mathematical proof technique is very useful in set theory, topology, plus other fields as well.
Question 4: What is the base case in mathematical induction?
Answer: As you know that mathematical induction is a technique of mathematical proof which we usually use to establish a certain statement that is for all natural numbers. We carry it out in two steps, the first one refers to the base case which is which we use to prove the certain statement for the first natural number.